I'm looking at a question to a practice exam. It states the following.

Imagine the universe is a spherical cavity at a temperature of 3K. Using this assumption, estimate the total number of photons in the universe.

Notes: integral[0->infinity,{x^2dx/(e^x-1)*dx}=2.4

black body energy density:

u = h_/(pi^2*c^3)*w^3/(e^((h_w/(kT))-1)

I need to find out the number of photons per unit volume (N/V). Once I have that, I can find what I'm looking for.

Any ideas on how to solve this?

Interesting problem.

Wien's radiation law will give you the energy density (energy / unit volume) for a given temperature in the interval [itex]\omega \rightarrow \omega + \delta\omega[/itex]. You should be able to determine from that the photon density. Then you have to estimate the size of the universe. Good luck!

I know this isn't what you want to hear, but I think that it is worth saying. In addition to the 'regular' photons, there are many more virtual photons. Virtual photons are real, just, by definition, don't have enough energy to be observable. These make up electromagnetic fields. Every electron, and negative charge spews out basically unlimited numbers of these photons.

Also, both quantum mechanics and now realitivity predict that space is full of nearly unlimited (the former) to at least some (later) energy, everywhere.

So if you don't know how to give them the answer that they want, just say its incalcuable for the reasons I have stated above.